Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids ; to which are Added, Elements of Plane and Spherical TrigonometryW.E. Dean, 1846 - 317 sider |
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Side 11
... equal , nor its angles right angles . 29. All other four sided figures besides these , are called trapeziums . 30 ... equal to the same thing are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If ...
... equal , nor its angles right angles . 29. All other four sided figures besides these , are called trapeziums . 30 ... equal to the same thing are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If ...
Side 12
... equal C D A B E ( 11. Definition ) to AB ; and because the point B is the centre of the cir- cle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are ...
... equal C D A B E ( 11. Definition ) to AB ; and because the point B is the centre of the cir- cle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are ...
Side 13
... equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given ...
... equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given ...
Side 14
... equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor . def . 3 ...
... equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor . def . 3 ...
Side 15
... equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . For , if AB be not ...
... equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . For , if AB be not ...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |
Vanlige uttrykk og setninger
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular plane polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 49 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 147 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 292 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 7 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 139 - K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their altitudes.
Side 33 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 79 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by...
Side 125 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 131 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.
Side 78 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.